[Author]
 Lodkin, A.A.; Manaev, I.E., Minabutdinov, A.R.

[Title]
 New results on amendments to the ergodic theorem for the Pascal automorphism
 

[AMS Subj-class]
 37A30 Ergodic theorems, spectral theory, Markov operators
 28A80 Fractals

[Abstract]
 Let $P$ be the Pascal-adic transformation. In 2004,  \'E.~Janvresse,
 T.~de~la~Rue and Y.~Velenik  considered random fluctuations of ergodic sums,
 for some cylindric functions non-cohomologous to a constant, viewed upon as
 graphs of functions of an integer argument on a segment of integers. These
 sums, linearly interpolated and properly renormalized, converge to (parts of)
 the graph of the well-known Takagi-Blancmange function. In  the above-mentioned
 work, a question has been raised whether this is true for a wider classes of
 functions.

 The paper generalizes these results and the results of A.Minabutdinov for the
 case of arbitrary ergodic invariant measures and answers several other
 questions.

[Keywords]
 Pascal automorphism, ergodic theorem, generalized Takagi function, Blancmange function,
 Walsh--Paley generalized system 

[Comments]
 Russian, 32 pp.

[Contact e-mail]
 aminabutdinov@gmail.com
 alodkin@gmail.com